Martin Flashman's Courses - Math 115 Summer, '04
Tentative Course Information- Subject to Change
Algebra and Elementary Functions
MTWR 1100-1220 SH 128
Office Hours: MTWR 12:30-1:40
Quiz #8 in class- Monday, August 2 !!!
Math 99 has been reinstalled!!! for summer 2004.
  • Prentice Hall Web Site for Assistance,etc. (This only works with Internet Explorer)
  • Course Assignments: Text Problem lists (Most recent)
  • Course Daily Schedule Plan (subject to change) 
  • Precalculus (and Calculus) websites
  • Math 095 modules at CSU Northridge (ALG II w/ geometry)
  • Algebra topics at the Purple Math website
  • Visual Calculus (Univ. of Tenn.) some pre-calculus tutorials, etc.
  • D.E. Joyce's  short introduction to Trigonometry (java  and web based)
  • New! Dave's Short Course on Complex Numbers This is an introduction to complex numbers (mathematics and a little bit of history as well).
  • Trig Java Applets Excellent Java applets that dynamically illustrate trigonometry.(International Education Software) 
  • Want to find out what your learning style is?

    • Here are two interesting learning styles inventories on the web: (1) NC State  (2)  Diablo Valley College .
  • Success in Mathematics (St.Louis University)
  • NEW! "How to suck up to your teacher." Homework Guidelines for Mathematics from Purple Math
  • Winplot (freeware for PC's that we will use) may be downloaded from Rick Parris's website or directly from Winplot .
  • Notes for Winplot authored by Al Lehnen (Madison Area Technical College in Madison, Wisconsin)

    • Back to Martin Flashman's Home Page :)

    OFFICE: Library 48     E-MAIL: flashman@humboldt.edu        PHONE:826-4950
    WWW: http://flashman.neocities.org/
    Hours (Tent.):  MTWR  12:40-1:40 (changed 6-24)       AND BY APPOINTMENT or by CHANCE!
  • PREREQUISITE: Math code 40 (or better) or permission.
  • Catalog Description: Functions and their graphs; in-depth treatment of exponential and logarithmic functions. Trigonometry: trigonometric functions, identities, solving triangles. Polynomial functions. Prerequisite: HSU MATH 42 or 44 or 45 or math code 40.
  • TEXT: Sullivan and Sullivan, Precalculus Enhanced with Graphing Utilities, third edition, Prentice-Hall, 2002. [The ISBN for the HSU custom order text is 0536684812.]
    PreCalculus (CD Collection) by Edward Burger, Thinkwell, 2001 (?)
  • SCOPE: We will cover topics primarily from the preliminaries and chapters 1-6 in S&S. Supplementary materials will be provided as appropriate.
  • TESTS and ASSIGNMENTS:  Homework assignments are made regularly. We will use Blackboard  to grade homework.

    • Homework results must be recorded on Blackboard by10:45 AM of the due date to receive credit.
  • I will discuss this further at the first class meeting. Assignments will be discussed in class on a daily basis.
  • The reality check quizzes, some done outside class on Blackboard and some in-class tests, will have similar problems. There will be at least three in-class tests (15-30 minutes). 
    • The final examination for the course will be comprehensive.
    It will be given in two parts on the last two classes of the term.
    MAKE-UP TESTS WILL NOT BE GIVEN EXCEPT FOR VERY SPECIAL CIRCUMSTANCES!
    It is the student's responsibility to request a makeup promptly,
    especially for  especially for unauthorized absence.
    *** DAILY ATTENDANCE SHOULD BE A HABIT*** 
  • GRADES: Final grades will be determined taking into consideration the quality of work done in the course as evidenced primarily from the accumulation of points from tests and various  assignments.

    • Reality Quizzes 1-7 Best 6 scores 600 points
    Reality Quiz 8 100 points
    Homework 200 points
    Final Examination 400 or 600 points
    Total 1300 or 1500  points
  • The final examination will be be worth either 400 or 600 points determined by the following rule:

    • The final grade will use the score that maximizes the average for the term based on all possible points.
    A grade of less than 50% on the final examination may result in a final grade of  F without offsetting high quality work on the other parts of the course.
  • Notice that only 400 or 600 of these points are from formal in-class examinations, so regular participation is essential to forming a good foundation for your grades as well as your learning.
  • MORE THAN 4 ABSENCES MAY LOWER THE FINAL GRADE FOR POOR ATTENDANCE.

    • ** Students wishing to be graded with either CR or NC should check with the . See the summer session course list for a full list of relevant days.
  • Technology: The computer or a graphing calculator can be used for many problems. We will use Winplot and Microsoft Xcel.
  • Graphing Calculators: Graphing calculators are welcome and highly recommended.
  • Use of  Office Hours and Math 99: Many students find  pre-calculus difficult because of weakness in their algebra background skills and concepts.  A grade of C in Math 44 might indicate this kind of weakness.

    • Difficulties that might have been ignored or passed over in previous courses can be a major reason for why things don't make sense now.

    You may use my office hours for some additional work on these background areas either as individuals or in small groups. My office time is  also available to discuss routine problems from homework after they have been discussed in class,  reality check quizzes, as well as using  technology.

    Math 99 has beenreinstalled!!! for summer 2004.  [6-1-04] You may consider registering for Math 99 Tutoring for Math 115. This is a 2 unit, credit/no credit "course" that provides generous tutorial assistance paid for by your registration. If you can afford the units, this is a good way to get help on specific problems.
    Regular use of my time outside of class or Math 99 should be especially useful for students having difficulty with the work and wishing to improve through a steady approach to mastering skills and concepts.

  • Don't be shy about asking for an appointment outside of the scheduled office hours


    • Math 115 Tentative Schedule [Subject to change and correction] 
    Week\Day 
    Monday
    		Tuesday
    Wednesday
    Thursday
    I. Introduction: Backgrounds and Key concepts
    		6-1 Introduction 
    What are Numbers? 
    Comparing Numbers:=,< 
    Number Operations, equations. (1.4)  [Cont'd on Wed.!]
    		 6-2 Sensible Precalc Ch 1.A
    Visualizing: numbers & intervals. 
    Sqr(2) is not a rational #. 
    The Pythagorean theorem. 
    Proofs of the Pythagorean Theorem 
    [Over 30 proofs !]
    [Many Java Applets proofs ]    		 6-3 Solving linear inequalities (1.5)
    Algebra review. App. A.1 
    Visualizing variables and plane coordinate geometry.
    II. Beginning Functions-Core functions and concepts. 
    Begin Right Triangle Trig    		 6-7 Plane Coordinates.
    More Geometry review: Midpoints.
    Similar triangles.
    Slopes of lines. 
    Review Polynomials. A.3 (Factoring)    		 6-8 More on graphs. Circles and Lines. What's a function? More on functions.  and linear functions.

    Practice Quiz    		 Graphs and mapping figures.
     Other function qualities.
     
    Quiz #1 - On-Blackboard Due by Tuesday 9 PM
    III. Triangle Trig
    6-14 Review of Key Triangles. 
    Overview of Core: trigonometric for Right Triangles
    Solving Right triangles.
    A.9 Properties of roots and exponents. 
    		Overview of Core: algebraic
    Secant lines and Linear Interpolation. 
    Triangle trig: Inverse trig acute
    		Primary Descriptive features of functions. 
    Law of Sines.
     Abs. value inequalities 
    Sine for obtuse angles. 
    		More law of sines 
    More Inverse trig (sine obtuse).
    Lab: Graphing Functions with Winplot.
    IV. Exponential functions 6-21 Radian measure and circles in general.
    Symmetry [wrt axes.]

    		Quiz #2 on-line due by 9pm Wed.
    Piecewise functions 
    Lab: Graphing and Trig Applets.? 
    Trig for obtuse angles. 
    Trig functions for all angles (sine and cosine)
    		Trig functions for all angles
    Start Law of cosines.
    Exponential Functions.
    Compound interest? 4.6(I) 

    Exponential functions and graphs.What is e? 4.2    		 Composed Mapping figures.
    More on law of cosines.
    Applications of triangle trig 
    V. Logarithmic functions More on Exponential Applications- compound interest and growth.
    ,    		   4.8 Logarithms: Introduction and definition. 
    G    raphs of exponential, logarithmic
    Basic properties of logs...  and applications and exponents-solving equations.
    		 Quiz #3 on-line- due 9pm 7-5-04
    More on properties of logs and exponents-
    The big picture on functions: Core functions and elementary functions
    Inverse tangent function.
    Graphs of sin and cos
    I.Trig function graphs NO Class July 4 Holiday
    		  sine & cosine functions.[LAB ]
    More on graphs of trig functions.
    More on Radian measure
    Circular Motion.
    		 graphs of  tan and sec.
    Logarithmic calculations in equations and computations. 
    . 
    		Quiz #4 on-line
    due by 9 pm 7-12

    Models using Exponential Functions

    More on graphs and basic properties of trig functions. 
    Graphs of tan and sec.    		  
    VII.Trig Equations 
    Trig Identities    		 Begin Trig Identities 
    Begin trig equations and review of 
     inverse trig functions 
     Logarithmic scales.Slide rules ?

    		 Slide rules
    Log scales and graphs.
    More exponential models.

    [***LAB ***]    		 Trig equations and review of 
     inverse trig functions (Asin and Acos)
    Brief  look at The Logistic
    More on graphs of trig functions, identities and equations.    		  Quiz #5
    NOW IN CLASS!
    More equations. 
    VIII. Graphs for inverse trig. 
    Addition formulae-     		More on Trig Identities: double angles!

    		Quiz #6 In class
    Double and half angles     		  Product to sum trig.Other Trig identities.  .
    IX.Polynomial and Rational Functions Quiz #7 on line
    Translation and scales for quadratics and 1/x.     		 More on quadratics.
    Graphs of polynomials 
    Complex numbers and trig
    More Trig functions and equations:
    graphs and elementary functions
    Begin Rational functions

    Long division and factors of polys. Roots and more on Polynomials.    		 More on  Complex Numbersand trig and complex roots! .
    MORE Polynomials- rational, real and complex roots!   Intermediate value theorem. 
    Bisection and Secant methods for estimating roots.
    Rational functions.Asymptotes.
    Difference quotients.    		  
    X. Pre-Calculus! Quiz #8 in class
    More on rational functions. 
    Combining trig Functions- lines review. Putting functions together.
    Composition & Inverse functions    		 Final comments on functions- algebraic and trignometric.
    "Tangents to graphs for logs and exponential functions. "?? A precalculus view. 
    Graphs using logarithmic scales.Example of using log and exp:log and log-log scales.    		  Final Exam Part I
    (40 minutes on Log and exponential functions.)
    		Final Exam Part II (80 minutes with very little from Part I)

    TentativeAssignments and Recommended Problems Tentative [Subject to change and correction] 
    SeeThe Prentice Hall Web Site
    Last updated: 
    Due Date
    SECTION
    Reading
    		 CD Viewing
    		 Assignments 
    		 Special Instructions & Interesting but Optional 
    HW #1
    6-2
         		1.4 Intro to Solving Equations.[9min]
    Solving a Linear Equaton. [8 min]
         		p43: 13-25 odd

    6-3
    		 Sensible Precalc Ch 1.A and Sensible Precalc Ch 1.B.1 Inequalities
    Intro to Solving Inequalities


    HW #2
    6-7
         		1.5
    Ch 1.B.1
    A.1         		Using the Cartesian System
    Finding the Distance between two Points.
         		p56: 13-59 odd
    Ch 1.B.1: 1(a,b), 3-7, 10, 14
    A.1 : 7,10,13,...43, 46 ( Every 3rd problem.)    		 Ch 1.B.1:  1c, 2, 16
    CD: Circles.
    HW #3
    6-8
         		A.2 read only. 
    Similar Triangles
    A.3.
    1.4
    1.1
         		Rationalizing Denominators
    Factoring....(what you want..)
    Triangles

         		A.3 : 3,11,19,27,39,47
    1.4: 31,41, 89
    p9: 1, 3; $$49, 29; 39

         		$$  For exercises 49 and 29, replace the given instructions by 
    a. plot the given points.
    b.Then, for the two given points, determine the distance: include the horizontal, vertical, and straight-line distances.
    c. determine and plot the midpoint
    HW #4
    6-9
    1.2
    1.6
    Sensible Precalc Ch 1.B.2 Read!
    		 Circles
    Graphing Equations
    Equations of a line.
    p19: 1, 5, 7, 8, 13, 19, 23
    p73: 71, 73, 59, 65, $$ 35, 39, 47, 53
    		 $$For problems 35, 39, 47, 53, Give the equation in slope intercept form and draw a graph and a transformation figure for the given information.
    HW #5
    6-10
    		 2.1
    1.6      		Function Basics
    Linear Functions- slope
    		 p96: 13abc, 15abc, 47, 85, 80
    1.6 p73:27-33 odd; 89,93

    HW #6
    6-14
    		 2.2 read only pp101-102, 107-108
    2.1    		 Function Basics
    Linear Functions- slope    		 p108: 1, 3, 5, 7, 31
    p 111: 33, 35
    p 96: 61, 63, 67, 69

    HW #7
    6-15
    		 A.9
    7.1 Only pp 528-529
    2.3 Only pp112-115      		Right Angle Trig.- Intro, Evaluating.
    		 p 1064: 1,7,25,31,33,36
    p536: $$(1-4)
    Do the reading FIRST! p123: 25,28,35     		$$ For 1-4 Find sine, cosine, and tangent for the given angle in the triangles.
    HW
    #8
    6-16
    A.9
    7.1 Read  pp530-532
    1.5 pp53-55     		Absolute Values- Solving equations, Solving inequalities,
    Right Angle trig.-Finding an angle...,Using trig..., finding the height...
    		 p 1064: 41-46, 53,57
    p536: 5-8, 21, 23, 35, 41
    p57: 73-85 odd

    HW #9
    6-17
    7.1
    2.3
    7.2 pages 539-542         		Function Basics-Notation
    Working w/funcions- determining intervals...
    Function Domain and Range- Finding...
    The Law of Sines- The law...Solving a triangle...
         		p536: 22,26,27, 37, 42, 43, 47, 52
    p122:  11, 13, 14, 15, 17
    p 547: 1-3, 5, 15, 29, 33
         		 
    HW #10
    6-21
    7.2 pages 543-546     		The Law of Sines- Solving a triangle... p 547: 9,11,13,17,23, 24, 31,39

    HW #11
    6-22
    7.1
    2.3 pp118-121
    5.1 pp 368-372
    		 Angles and radian Measure:
    Finding the quadrant...Converting...
    		 p536: 31,33, 39, 49, 57, 61
    p379: 1- 35 odd     		For LAB  p123:37-43.
    HW #12
    6-23
    5.2
    2.4 p128-131
    		 The trig functions: trig functions of important angles
    Graphing Functions: graphing piecewise...
    		 p132:15,16,19,27
    p 395: (1,3,7 find sine and cosine only), 9,10, 23,(    39, 43- find sine and cosine only)

    HW #13
    6-24
    4.2
    7.3 through Ex. 1
    		p 395: 1,3,7, 39, 43find tangent and secant only
    p 297: 1-5,  See $$ for 19-22,25
    p555: 1-3, 25    		 $$ For 19-22,25:Ignore the text instruction. For each function make a table of values, a transformation figure, and a graph.
    HW #14
    6-28
    		  4.2
    7.3 Ex.2&3    		  Exponential Functions:
    Intro to, Graphing... Useful... and More...
    The Law of cosines: The law.., (SAS), SSS
    		 p 297: 4, 5,  11-18,37, 38; $$29-34
    p555: 7, 13, 21, 27, 28, 31      		$$ For 29-34:Ignore the text instruction. For each function make a table of values, a composed transformation figure, and a graph.
    HW#15
    6-29
    		 4.2
    4.6 pp327-330
    		 The number e: e
    Applying Exponential Functions; using properties...
         		p 297: 7, 9, 65, 42, 61
    p335: 1, 3,5, 7, 9, 21, 25, 27, 11

    HW#16
    6-30
    		 4.3 pp301-304
    4.6 p335 Ex.2
    		 Logarithmic functions: Intro, Converting p310: 1, 11, 13, 19, 24 - 31, 35, 36, 97,99
    p 336: 33

    HW#17
    7-1 to 7-6
    		 4.3 pp307-308
    4.4
    5.4 pp414-419
    2.5 pp148-151
    		 Properties of Logs
    Evaluating Logs
    Solving Exponential and Log equations
    Applying ... Compund interest
    Composite Functions: Operations...,composite...,Components of..
    		 p310: 37-39,42,43,47,48; 85-94,101, 103,111
    p321:3, 5, 6, 9, 25, 31, 39, 45, 51    ; 61, 62
    p155: 1,5

    HW#18
    7-7
    		5.4

    		 Graphing Sine and Cosine:: Intro..., Graphing
    Graphing .. with shifts: ... phase shifts. Fancy...

    		 p 426: $$ (13,17, 21), 39-47

    		 $$ For 13, 17, and 21:Ignore the text instruction. For each function make a table of values, a composed transformation figure, and a graph.
    HW #19
    7-8
    4.5 & 4.3 pp307-309
    5.5         		Solving Exponential and Log equations
    Graphing other trig: ... the Tangent...
    p311: 85, 87, 91, 93; 
    p327: 1, 5, 9, 11, 12
    p 435: 1-14
    p 426: 1-10,  $ (29-33 odd), $$( 15, 24, 53)    		 $ For 29-33 odd :Ignore the text instruction. Graph each function. 
    $$ For 15, 25, and 53: Ignore the text instruction.  For each function make a table of values, a composed transformation figure, and a graph.
    HW #20
    7-12
    5.3
    5.5
    5.6: pp437-440
    5.1 p377-378
    4.7         		Word problems involving Growth and Decay; Introduction
    Angles and radian Measure: Uing the arc Length Formula
    Graphing Sine..: Fancy Graphing: Changes in period...
         		p411: 1 - 7odd,17-23 odd
    p446: 1,3,13, 17
    p380: 81,87,89,97,99
    p347: 1, 2, 3

    HW #21
    7-13
    5.2 pp393-394
    5.3         		Basic Trig Identities: Fundamental...
    Proving Trig Identities: Proving...
    		 p396: 73-75
    p411: 67-77odd;49-53; 103-104

    HW #22
    7-14
         		4.7
    6.3 pp477-478
    6.1: pp 458-465
    		 Word problems involving growth:  Intro to expon...,Half Life
    Newton's Law of Cooling
         		p347: 5, 9, 11
    p480:1-10
    p468: 1-11 odd, 13-15, 45, 47

    HW
    #23
    7-15
    		 6.3
    6.7 pp 507-509
    		p511: 1-5
    p 480: 11,14,17,20,...,41 (every 3rd problem), 81, 85

    HW #24
    7-19
         		6.3
    6.7
         		Solving trig Equations: Solving...
         		p 511: 11-19 odd, 35-37
    p480: 51, 54, 57,... , (every 3rd problem) ,78

    HW#25
    7-20
    6.1 (especially graphs)
    6.2  pp470-472
    6.4 pp482-486
    		 Inverse Trig Functions:  An Intro...,
    Evaluating the composition...
    The Sum and Difference Identities: Identities...
    		 p468: 25-27, 33-35,49
    p474: 1-9odd; 13,19

    		 Look at This PAGE on the web!
    HW #26
    7-21
         		6.4 pp482-486
    6.5 pp493-494
         		Double-Angle Identities: Confirming..., Using....
    		 p 491: 1-4, 13-21 odd
    p501: [1, 2, 7 DO a and b only].    		 great web resource for trig with java (manipula math products)
    HW#27
    7-22
    6.4 pp486-489
    6.5. pp498-500
    		p 491: 23,24,31,32,41
    p501: [1,2,7] DO c and d only. 13,14, 51,53, 59, 60

    HW#28
    7-26
    		 6.6 pp503-504
    		p505:1,2
    p 491:  7, 43, 53, 55, 59, 81 
    p 501: 15, 45, 67

    HW#29
    7-27
         		2.4
    2.5
    3.1 pp174-182
    A3 Polynomial algebra (Review!)

    		 Quadratic Functions- Basics
         		p145: 1-12, 23, 41, 51, 63ef
    p189: 1-8, 9,11,13,15,25-28
    p 1012: 3, 11,19,23,27,35 ,39,47, 63

    HW#30
    7-28
         		3.1 pp182-187
    3.2 pp 195-198 middle
    A7  Complex Numbers, etc.
         		Quadratic functions- The vertex.
    Quadratic Equations and the Quadratic Formula
         		p 189: 31,33,37,43,49,53,55,65, 69,73,81
    p211: 1-13

    HW #31
    7-29

    		 A5 Polynomial Division
    3.3 pp203-205 (zeroes and multiplicity on graphs)
    3.7  pp245-247(remainder and factor theorems)
    		 Polynomials- Long Division
    The remainder Theorem
    The factor Theorem
         		p211: 1-13
    p 1028: 1-5, 19-21, 23, 24
    p211 : 17, 18, 19-25odd (a,b only), 65
    p257:1-5,73


    HW#32
    8-2
         		2.1
    3.7
    3.8
    3.4
    		p99: 73-79, 83,85
    p263:1-5 odd, 11, 17, 35, 36
         		read more on-line about Complex Numbers or App.7
    Inventory



    		85








    		5.1 pp 372-377
    		p379: 37-39, 45-47, 53, 55


    		4.6 pp331-335 (New- 7-2-03)
    		p336: 11,29,37,47


    		4.4
    		p321:  75, 77, 79


    		4.5
    		p311:  98;  p327: 17, 19, 21, 23, 29; 13, 15


    		4.5
    		p327: 3, 14, 49, 53


    		4.7
    		p347: 4, 12a,b,c, 13a,b,c, 15a


    		REVIEW
    		p361: 11,13-16, 21-24,27,31,33,35,39,$$(43,51), 53,59,79,83 $$ For 43 and 51: Ignore the text instruction.  For each function make a table of values, a composed transformation figure, and a graph.

    5.4
    		p 426: 1-10,  $ (29-33 odd), $$( 15, 24, 53) $ For 29-33 odd :Ignore the text instruction. Graph each function. 
    $$ For 15, 25, and 53: Ignore the text instruction.  For each function make a table of values, a composed transformation figure, and a graph.

    5.5
    		p435: 1-10; 19, 21, 23, 35


    		5.3 pp399-404;409-410




    REVIEW
    		p452:1-11 odd, 47, 48, 59, 60, 79, 83, 85 
    p574: 19, 21, 51


    5.5 
    5.6: pp437-440
    		p446: 1,3,13, 17


    6.1
    6.2
    		p468: 25-27, 33-35,49
    p474: 1-9odd; 13,19


    6.7




    6.3
    		p 480: 1-10
    p474:29, 33, 37


    		6.8 pp513-514
    		p518: 1, 3,4,7


    		3.7 p248-251 (rational and real roots)
    		p257: 11-17 odd, 29, 53


    		3.7 pp255-6
    		p258: 33,35,63, 65


    		3.8 
    		p263:1-5 odd, 11, 17, 35, 36


    		3.4 
    		p224: 1-7 odd; $$ (23, 29,30, 31); 35 $$ For 23, 29, 30, and 31 : Ignore the text instruction.  For each function make a table of values, a composed transformation figure, and a graph.
    read more on-line about Complex Numbers or App.7

    		2.3 
    		p 123: 25-35 odd; 59-65 odd


    		4.1 inverses
    		p284: 1-5,9-11, 15-17, 21-25odd,31-39 odd


    		 1.5
    3.5
    		p. 57:  67, 69
    p 234: 1,9, 27


    		Review
    		p167: 1-3,7,18,19, 23,29,35, 61,65,67


    		Review for Final
    		p 580: 1,3,4,5,6,8,9,11,12,13


    		 




    		 




    		5.4 p419-425
    		p427: 49-56; 63-65; 85,86


    		2.5 
    		p145: 17-22, 25ab, 33, 37, 39, 55, 63abcd


    3.1 
    p189: 1-8, 25, 29, 33, 35, 37, 73


    2.6 
    p155: 1, 5, 13, 19, 35, 51


    4.1 
    p285: 15, 21, 31, 33, 35, 55, 61


    2.7, 3.1
    p194: 87, 75; p163: 1, 13, 23

    Back to Martin Flashman's Home Page :)
    Back to HSU Math. Department :}